A hyper-elastic thermal aging constitutive model for rubber-like materials Ahmed G Korba 1 , Abhishek Kumar 1 and Mark Barkey 1 Abstract Different phenomenological, empirical, and micromechanical constitutive models have been proposed to describe the behavior of incompressible isotropic hyper-elastic materials. Among these models, very few have accounted for the thermal aging effect on the model constants and parameters. This article introduces a new empirical con- stitutive hyper-elastic model for thermally aged hyper-elastic materials. The model named “the weight function based (WFB) model” considers the effect of aging tem- perature and time on its parameters. The WFB model formulation can facilitate fatigue analysis and lifetime prediction of rubber-like materials under aging conditions. The WFB model in this article defines all rubber-like material properties, such as fracture stretch, strength, and stiffness, by predicting the full stress–strain curve at any aging time and temperature. The WFB model was tested on natural rubber for uniaxial and biaxial loading conditions. More than 100 specimens were aged and tested uniaxially under various temperatures and aging times to extract the stress–strain behavior. The temperatures used in the test ranged from 76.7  C to 115.5  C, and the aging time ranged from 0 to 600 hours (hrs). A classical bulge test experiment was generated to extract the biaxial natural rubber material behavior. An ABAQUS finite element analysis model was created to simulate and verify the generated biaxial stress–strain curve. The proposed model represents the aging effect on the tested natural rubber under uniaxial and biaxial loading conditions with an acceptable error margin of less than 10% compared to experimental data. Keywords Hyper-elasticity, thermal aging, rubber-like, weight function based, uniaxial, biaxial, bulge 1 Department of Aerospace Engineering and Mechanics, The University of Alabama, Tuscaloosa, AL, USA Corresponding author: Ahmed G Korba, Department of Aerospace Engineering and Mechanics, The University of Alabama, Tusca- loosa, AL 35487, USA. Email: agkorba@crimson.ua.edu Journal of Elastomers & Plastics 1–24 ª The Author(s) 2019 Article reuse guidelines: sagepub.com/journals-permissions DOI: 10.1177/0095244319883405 journals.sagepub.com/home/jep